Question

The angle of elevation of a 40m high tower from the foot of a building is 60°. The angle of elevation of the top of the building from the foot of the tower is 30°. Find the height of the building​

Answer 1

Answer:

The angle of elevation of the top of building at a point on the level ground is 45degree . After moving 200m towards the building along the same horizontal line, the angle of elevation of the building is 60degree . Find the height of the building.

Step-by-step explanation:

The angle of elevation of the top of building at a point on the level ground is 45degree . After moving 200m towards the building along the same horizontal line, the angle of elevation of the building is 60degree . Find the height of the building.The angle of elevation of the top of building at a point on the level ground is 45degree . After moving 200m towards the building along the same horizontal line, the angle of elevation of the building is 60degree . Find the height of the building.The angle of elevation of the top of building at a point on the level ground is 45degree . After moving 200m towards the building along the same horizontal line, the angle of elevation of the building is 60degree . Find the height of the building.

The angle of elevation of the top of building at a point on the level ground is 45degree . After moving 200m towards the building along the same horizontal line, the angle of elevation of the building is 60degree . Find the height of the building.The angle of elevation of the top of building at a point on the level ground is 45degree . After moving 200m towards the building along the same horizontal line, the angle of elevation of the building is 60degree . Find the height of the building.The angle of elevation of the top of building at a point on the level ground is 45degree . After moving 200m towards the building along the same horizontal line, the angle of elevation of the building is 60degree . Find the height of the building.

Answer 2

height of the building is 10.33 metres

Question :

The angle of elevation of a 40m high tower from the foot of a building is 60°. The angle of elevation of the top of the building from the foot of the tower is 30°. Find the height of the building.

Given :

Length of the tower = 40m

Angle of elevation from foot of the tower to the top of the building = 30°

Angle of elevation from the foot of the building to the top of the tower = 60°

Let's have :

Length of the building = h

distance between building and tower = x

Formula applied :

$tan = \frac{opposite \: side \: }{adjacent \: side}$

Solution :

we know that,

$tan60 = \sqrt{3}$

$\frac{opposite \: side}{adjacent \: side \: } = \frac{40}{x}$

equalize the above values,

$\sqrt{3} = \frac{40}{x}$

$x = \frac{40}{ \sqrt{3} }$

Now have values of tan30°,

$tan30 = \frac{1}{ \sqrt{3} }$

$\frac{opposite \: side}{adjacent \: side} = \frac{h}{x}$

equalize the values,

$\frac{1}{ \sqrt{3} } = \frac{h}{x}$

substitute the value of x,

$\frac{1}{ \sqrt{3} } = \frac{h}{ \frac{40}{ \sqrt{3} } }$

$h = \frac{1}{ \sqrt{3} } \times \frac{40}{ \sqrt{3} }$

$h = \frac{40}{3}$

$h = 10.33$